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Abstract
In case of tunnels with arbitrary geometries, solutions for stresses and displacements
in the tunnel exterior might be derived with the aid of the conformal mapping technique of the complex variable method. Thereby, the physical tunnel domain is mapped onto a fictitious unit circle domain on which the elastic potentials, as part of the final solution, are evaluated. The used mapping function involves complex mapping coefficients. In this paper an overview of analytical solutions
for stress and displacements fields around tunnels is provided, from the early Kirsch solution to the solutions involving the complex variable theory and conformal mapping. A possible solution procedure for the determination of these mapping coefficients based on an iterative process including the solution of linear systems of equations is presented. The proposed solution procedure can be
utilized for the determination of the mapping coefficients of various conformal mapping functions as defined in different closed-form solutions.
in the tunnel exterior might be derived with the aid of the conformal mapping technique of the complex variable method. Thereby, the physical tunnel domain is mapped onto a fictitious unit circle domain on which the elastic potentials, as part of the final solution, are evaluated. The used mapping function involves complex mapping coefficients. In this paper an overview of analytical solutions
for stress and displacements fields around tunnels is provided, from the early Kirsch solution to the solutions involving the complex variable theory and conformal mapping. A possible solution procedure for the determination of these mapping coefficients based on an iterative process including the solution of linear systems of equations is presented. The proposed solution procedure can be
utilized for the determination of the mapping coefficients of various conformal mapping functions as defined in different closed-form solutions.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of the 15th International ISRM Conference 2023 & 72nd Geomechanics Colloquium |
| Subtitle of host publication | Challenges in Rock Mechanics and Rock Engineering |
| Editors | Wulf Schubert, Alexander Kluckner |
| Place of Publication | Salzburg |
| Publisher | Austrian Society for Geomechanics |
| Pages | 1793-1798 |
| Number of pages | 6 |
| ISBN (Electronic) | 978-3-9503898-3-8 |
| Publication status | Published - 10 Oct 2023 |
| Event | 15th ISRM Congress 2023 & 72nd Geomechanics Colloquium - Congress Salzburg, Salzburg, Austria Duration: 9 Oct 2023 → 14 Oct 2023 https://www.isrm2023.com/de/ |
Conference
| Conference | 15th ISRM Congress 2023 & 72nd Geomechanics Colloquium |
|---|---|
| Abbreviated title | ISRM 2023 |
| Country/Territory | Austria |
| City | Salzburg |
| Period | 9/10/23 → 14/10/23 |
| Internet address |
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An iterative scheme for the determination of the conformal mapping coefficients used in closed-form solutiosn for tunnels with arbitrary geometry
Manuel Winkler (Speaker)
10 Oct 2023Activity: Talk or presentation › Poster presentation › Science to science
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15th ISRM Congress 2023 & 72nd Geomechanics Colloquium
Manuel Winkler (Participant), Paul Johannes Unterlaß (Participant), Thomas Geisler (Participant), Thomas Marcher (Chair), Thomas Frühwirt (Chair), Philipp Dobita (Participant), Mario Wölflingseder (Participant), Vaibhav Shringi (Participant), Alla Sapronova (Participant), Anton Kaufmann (Participant), Manfred Blümel (Participant) & Abdallah Ahmed Fouad Elsayed Soliman (Participant)
10 Oct 2023 → 13 Oct 2023Activity: Participation in or organisation of › Conference or symposium (Participation in/Organisation of)